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Countdown to 150
Limiting Factors, Competitive Exclusion, and a More
Expansive View of Species Coexistence
Mark A. McPeek*
Dartmouth College
The first American Naturalist appeared in March 1867.
In a countdown to the 150th anniversary, the editors
have solicited short commentaries on articles from the
past that deserve a second look.
When I began graduate school in the 1980s, species interactions were viewed predominantly through the prism
of resource competition. Species found together were
largely understood to coexist because of how they segregated their use of the available spectrum of local resources.
I entered this world of ideas wholeheartedly, but I was
fascinated by why prey species are able to coexist with
some predators and not others. Consequently, the central
concept of my scientific discipline, Hutchinson’s niche,
seemed to have no bearing on my ecological fascinations.
Predation was understood largely as a species interaction
that ameliorated the effects of resource competition among
the prey, and so its main consequence was to prevent
competitive exclusion (Paine 1966).
In struggling to make sense of all this, I came across an
article by Simon A. Levin in The American Naturalist
(Levin 1970) that was a revelation to me. In it, Levin
articulated many of my own misgivings about having resource competition as the sole basis for understanding
species coexistence, and he offered a new vantage from
which community organization could be understood.
The article begins with a presentation of the ideas underlying Gause’s principle of competitive exclusion—the
conceptual basis of Hutchinson’s definition of the niche
(1957, “Concluding remarks,” Cold Spring Harbor Symposium of Quantitative Biology 22:415–427). The article is
the epitome of scholarship, using many quotes from the
relevant articles to build his argument. The motivation for
the argument is Slobodkin’s 1961 analysis of Gause’s competitive exclusion principle and his evaluation of its test* E-mail: [email protected].
Am. Nat. 2014. Vol. 183, pp. iii–iv. 䉷 2014 by The University of Chicago.
0003-0147/2014/18303-55153$15.00. All rights reserved.
DOI: 10.1086/675305
ability (found in Growth and Regulation of Animal Populations, Holt, Rinehart & Winston, New York). Levin
draws on Slobodkin’s logical arguments to show that
Gause’s competitive exclusion principle results in a tautology. If the ecological niche is defined “as that space
which no two species can continue to occupy for an indefinitely long period of time” (Slobodkin 1961), “no one
can any longer dispute the Gause principle” (Levin 1970,
p. 414).
He motivates the main analysis presented in the article
by arguing that Hutchinson’s “hypervolumes in multidimensional space” are not incorrect representations of species niches, but rather, we are incorrect in how we characterize the importance of various dimensions constituting
a species’ hypervolume and the relationships between the
hypervolumes for multiple species:
Which dimensions those are is determined by which
factors are limiting those species, be those factors
resources, predators, or others. Two species cannot
coexist unless their limiting factors differ and are
independent; this is the only criterion one need examine at a given time and place. (Levin 1970, p.
415)
This is a much more inclusive concept, embracing not
only competition for food but also predation and any other
type of interaction that may be important to a species.
Also, the emphasis shifts the focus to factors that limit the
abundance of each species. The implication here is that
two species may have identical Hutchinsonian hypervolumes but still coexist if their abundances are limited by
the factors associated with different dimensions of that
hypervolume.
A general mathematical treatment of a community of
interacting species is developed to make a simple but profound point. The population dynamics of each species is
governed by a general equation that is a function of the
abundances of the species in the system and variables defined by factors extrinsic to the community (e.g., abiotic
variables; eq. [1] in Levin 1970). All of the contributing
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iv The American Naturalist
terms in this function define the “limiting factors” for that
species, and these limiting factors can be thought of singly
or in combinations.
The article offers a simple mathematical proof to answer
the primary question of how large must the minimum set
of limiting factors be for a community of r species to
coexist at either a stable point equilibrium or a stable limit
cycle. The direct implications of this proof is the main
result of the article: “In particular, no stable equilibrium
is possible if some r species are limited by less than r
factors” (Levin 1970, p. 419).
Along the way to this result, the nature of limiting factors, point equilibria versus limit cycles, perturbation analyses, deterministic versus random environments, and various forms of stability are discussed. In particular, the
proof applies to all types of limiting ecological factors and
not just resource limitation, and the conclusions apply
equally well to systems with stable point equilibria and
stable limit cycles.
The article concludes by first offering a reinterpretation
of Paine’s (1966) classic experiments. Typically, Pisaster
predation is described as preventing competitive exclusion
by Mytilus mussels of a number of inferior competitors
(Paine 1966), but Levin shifts the focus to changes in sets
of limiting factors. “Presumably, the presence of Pisaster
had made possible the independent operation of a great
many more limiting factors than was possible without Pisaster. In its absence, species which no longer had to contend with predation were now able to dominate several
resources that could previously be divided among more
species” (Levin 1970, p. 419).
The application of the main result to a number of ecological situations is then proffered. Neutral community
dynamics is presaged in a discussion of dynamics when a
system is short of limiting factors. Finally, the article deals
with how predation and resource competition may interact
to promote coexistence or limit community membership
in a basic outline that foreshadows results on diamondshaped and apparent-competition community modules.
Throughout my career, this article has been a touchstone
to which I have returned continually. On first reading, it
provided me with an alternative way to think about species
coexistence unconstrained by resource competition. A decade later it provided me insights about what is required
for coexistence of consumers that simultaneously compete
for resources and are fed on by a common predator. Most
recently, it offered me inspiration for why “intraspecific
competition must be greater than interspecific competition” was an insufficient mindset for understanding coexistence.
Our conception of species coexistence in biological
communities has moved far beyond the simplistic formulations based largely (or solely) on resource competition. However, the competitive exclusion principle and
Hutchinson’s niche concept still have a powerful hold on
how we view nature and interpret species interactions. For
me, the perspective that Levin (1970) first articulated is a
conceptually richer and mathematically stronger foundation on which our queries about biological communities
should be based. The question is not whether two species
that are limited by the same set of factors can coexist.
Rather, the correct question is whether these species differ
in how they are limited by the same set of factors.
Finally, I also greatly admired this article for its sense
of whimsy and humor. Too often science is dry, stiff, and
humorless. To prove that it does not have to be so, I end
by quoting from Levin’s “Acknowledgments,” and I draw
your attention to the mathematician’s joke at the end of
the first sentence: “Finally, this paper cannot close without
an exposition of certainly the most elegant form of the
niche theorem (section 1) to appear anywhere (unfortunately without proof). The following is taken from Dr.
Seuss’s epic On Beyond Zebra (Geisel 1955 [Random
House, New York]).
And NUH is the letter I use to spell Nutches
Who live in small caves, known as Nitches, for hutches.
These Nutches have troubles, the biggest of which is
The fact there are many more Nutches than Nitches.
Each Nutch in a Nitch knows that some other Nutch
Would like to move into his Nitch very much.
So each Nutch in a Nitch has to watch that small Nitch
Or Nutches who haven’t got Nitches will snitch.
“W. L. Brown Jr. and R. Root were aware of this statement
long before the author, but it should indeed have wider
currency.”
In The American Naturalist
Levin, S. A. 1970. Community equilibria and stability, and an extension of the competitive exclusion principle. American Naturalist
104:413–423.
Paine, R. T. 1966. Food web complexity and species diversity. American Naturalist 100:65–76.
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All use subject to JSTOR Terms and Conditions